{"id":6053,"date":"2025-07-05T12:23:29","date_gmt":"2025-07-05T04:23:29","guid":{"rendered":"https:\/\/nullthought.net\/?p=6053"},"modified":"2025-07-05T12:23:31","modified_gmt":"2025-07-05T04:23:31","slug":"%e6%b5%85%e8%b0%88arima%ef%bc%88autoregressive-integrated-moving-average%ef%bc%8c%e8%87%aa%e5%9b%9e%e5%bd%92%e6%bb%91%e5%8a%a8%e5%b9%b3%e5%9d%87%e6%95%b4%e5%90%88%e6%a8%a1%e5%9e%8b%ef%bc%89","status":"publish","type":"post","link":"https:\/\/nullthought.net\/?p=6053","title":{"rendered":"\u6d45\u8c08ARIMA\uff08AutoRegressive Integrated Moving Average\uff0c\u81ea\u56de\u5f52\u6ed1\u52a8\u5e73\u5747\u6574\u5408\u6a21\u578b\uff09"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">ARIMA\uff08AutoRegressive Integrated Moving Average\uff0c\u81ea\u56de\u5f52\u6ed1\u52a8\u5e73\u5747\u6574\u5408\u6a21\u578b\uff09\u662f\u65f6\u5e8f\u6570\u636e\u5206\u6790\u4e0e\u9884\u6d4b\u4e2d\u6700\u7ecf\u5178\u3001\u5e7f\u6cdb\u5e94\u7528\u7684\u7edf\u8ba1\u5efa\u6a21\u65b9\u6cd5\u4e4b\u4e00\u3002\u5b83\u7279\u522b\u9002\u7528\u4e8e<strong>\u5177\u6709\u8d8b\u52bf\u6027\u4f46\u975e\u5b63\u8282\u6027<\/strong>\u7684\u65f6\u95f4\u5e8f\u5217\u3002<\/p>\n\n\n\n<h5 class=\"wp-block-heading\">\u4e00\u3001ARIMA\u6a21\u578b\u57fa\u672c\u539f\u7406<\/h5>\n\n\n\n<p class=\"wp-block-paragraph\">ARIMA\u6a21\u578b\u7684\u76ee\u6807\u662f\u5bf9<strong>\u4e00\u7ef4\u65f6\u5e8f\u6570\u636e<\/strong>\u8fdb\u884c\u5efa\u6a21\u4e0e\u9884\u6d4b\u3002\u5b83\u5047\u8bbe\u672a\u6765\u503c\u662f\u8fc7\u53bb\u503c\uff08\u81ea\u56de\u5f52\u90e8\u5206\uff09\u3001\u8fc7\u53bb\u8bef\u5dee\uff08\u6ed1\u52a8\u5e73\u5747\u90e8\u5206\uff09\u4ee5\u53ca\u5dee\u5206\u8f6c\u5316\u540e\u6570\u636e\u7684\u7ec4\u5408\u3002\u9002\u5408\u7528\u4e8e<strong>\u5e73\u7a33\u6216\u53ef\u5dee\u5206\u5e73\u7a33\u7684\u65f6\u95f4\u5e8f\u5217\u6570\u636e<\/strong>\u5efa\u6a21\u3002<\/p>\n\n\n\n<h5 class=\"wp-block-heading\">\u4e8c\u3001\u6a21\u578b\u7ed3\u6784\u4e0e\u547d\u540d\uff1aARIMA(p, d, q)<\/h5>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>p\uff08AutoRegressive\uff0c\u81ea\u56de\u5f52\u9636\u6570\uff09<\/strong>\uff1a\u8868\u793a\u6a21\u578b\u4f7f\u7528\u524dp\u4e2a\u65f6\u95f4\u70b9\u7684\u6570\u636e\u8fdb\u884c\u9884\u6d4b\u3002<\/li>\n\n\n\n<li><strong>d\uff08Integrated\uff0c\u5dee\u5206\u9636\u6570\uff09<\/strong>\uff1a\u8868\u793a\u4e3a\u4e86\u4f7f\u65f6\u95f4\u5e8f\u5217\u5e73\u7a33\uff0c\u9700\u8981\u8fdb\u884c\u591a\u5c11\u9636\u5dee\u5206\u3002<\/li>\n\n\n\n<li><strong>q\uff08Moving Average\uff0c\u79fb\u52a8\u5e73\u5747\u9636\u6570\uff09<\/strong>\uff1a\u8868\u793a\u6a21\u578b\u4f7f\u7528\u524dq\u4e2a\u9884\u6d4b\u8bef\u5dee\u5bf9\u5f53\u524d\u503c\u8fdb\u884c\u4fee\u6b63\u3002<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">ARIMA\u6a21\u578b\u53ef\u4ee5\u8868\u793a\u4e3a\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"819\" height=\"274\" src=\"https:\/\/nullthought.net\/wp-content\/uploads\/2025\/07\/image-4.png\" alt=\"\" class=\"wp-image-6054\" srcset=\"https:\/\/nullthought.net\/wp-content\/uploads\/2025\/07\/image-4.png 819w, https:\/\/nullthought.net\/wp-content\/uploads\/2025\/07\/image-4-300x100.png 300w, https:\/\/nullthought.net\/wp-content\/uploads\/2025\/07\/image-4-768x257.png 768w\" sizes=\"auto, (max-width: 819px) 100vw, 819px\" \/><\/figure>\n\n\n\n<ul class=\"wp-block-list\"><\/ul>\n\n\n\n<h5 class=\"wp-block-heading\">\u4e09\u3001\u5efa\u6a21\u6d41\u7a0b\u8be6\u89e3<\/h5>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u6570\u636e\u9884\u5904\u7406<\/strong>\uff1a\n<ul class=\"wp-block-list\">\n<li>\u7f3a\u5931\u503c\u5904\u7406\uff1b<\/li>\n\n\n\n<li>\u5904\u7406\u5f02\u5e38\u503c\uff08\u53ef\u9009\uff09\uff1b<\/li>\n\n\n\n<li>\u53ef\u89c6\u5316\u521d\u6b65\u89c2\u5bdf\u8d8b\u52bf\u548c\u5b63\u8282\u6027\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>\u5e73\u7a33\u6027\u68c0\u9a8c<\/strong>\uff1a\n<ul class=\"wp-block-list\">\n<li><strong>ADF\u68c0\u9a8c\uff08Augmented Dickey-Fuller\uff09<\/strong>\uff1a\u68c0\u9a8c\u5e8f\u5217\u662f\u5426\u5177\u6709\u5355\u4f4d\u6839\u3002<\/li>\n\n\n\n<li>\u82e5\u975e\u5e73\u7a33\uff08\u4f8b\u5982\u5b58\u5728\u8d8b\u52bf\uff09\uff0c\u5219\u8fdb\u884c\u5dee\u5206\uff08d \u6b21\uff09\u76f4\u5230\u5e73\u7a33\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>\u8bc6\u522b\u6a21\u578b\u53c2\u6570 (p, d, q)<\/strong>\uff1a\n<ul class=\"wp-block-list\">\n<li>\u4f7f\u7528<strong>ACF\uff08\u81ea\u76f8\u5173\u51fd\u6570\uff09\u548cPACF\uff08\u504f\u81ea\u76f8\u5173\u51fd\u6570\uff09\u56fe<\/strong>\u5224\u65ad p \u548c q\uff1a\n<ul class=\"wp-block-list\">\n<li>PACF \u622a\u5c3e \u2192 AR(p)\uff1b<\/li>\n\n\n\n<li>ACF \u622a\u5c3e \u2192 MA(q)\uff1b<\/li>\n\n\n\n<li>\u90fd\u622a\u5c3e \u2192 ARMA\uff1b<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u82e5\u5e8f\u5217\u660e\u663e\u975e\u5e73\u7a33\uff0c\u5219 d \u2265 1\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>\u6a21\u578b\u62df\u5408<\/strong>\uff1a\n<ul class=\"wp-block-list\">\n<li>\u9009\u62e9\u591a\u4e2a (p,d,q) \u7ec4\u5408\u62df\u5408\u6a21\u578b\uff0c\u4f7f\u7528\u4fe1\u606f\u51c6\u5219\u5982 AIC\u3001BIC \u8fdb\u884c\u6bd4\u8f83\uff1b<\/li>\n\n\n\n<li>\u62df\u5408\u65b9\u6cd5\u4e00\u822c\u4e3a\u6700\u5927\u4f3c\u7136\u4f30\u8ba1\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>\u6a21\u578b\u8bca\u65ad<\/strong>\uff1a\n<ul class=\"wp-block-list\">\n<li>\u68c0\u67e5\u6b8b\u5dee\u662f\u5426\u662f\u767d\u566a\u58f0\uff08Ljung-Box \u68c0\u9a8c\uff09\uff1b<\/li>\n\n\n\n<li>\u68c0\u67e5\u6b8b\u5dee\u56fe\u662f\u5426\u6709\u6a21\u5f0f\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>\u9884\u6d4b<\/strong>\uff1a\n<ul class=\"wp-block-list\">\n<li>\u4e00\u65e6\u6a21\u578b\u901a\u8fc7\u8bca\u65ad\uff0c\u5373\u53ef\u4f7f\u7528\u5176\u8fdb\u884c\u672a\u6765\u82e5\u5e72\u6b65\u7684\u9884\u6d4b\uff1b<\/li>\n\n\n\n<li>\u540c\u65f6\u53ef\u8f93\u51fa\u9884\u6d4b\u533a\u95f4\uff08\u7f6e\u4fe1\u533a\u95f4\uff09\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\u56db\u3001\u53c2\u6570\u542b\u4e49\u548c\u6570\u5b66\u5f62\u5f0f<\/h3>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"734\" height=\"446\" src=\"https:\/\/nullthought.net\/wp-content\/uploads\/2025\/07\/image-5.png\" alt=\"\" class=\"wp-image-6055\" style=\"width:444px;height:auto\" srcset=\"https:\/\/nullthought.net\/wp-content\/uploads\/2025\/07\/image-5.png 734w, https:\/\/nullthought.net\/wp-content\/uploads\/2025\/07\/image-5-300x182.png 300w\" sizes=\"auto, (max-width: 734px) 100vw, 734px\" \/><\/figure>\n\n\n\n<h5 class=\"wp-block-heading\">\u4e94\u3001ARIMA\u6a21\u578b\u4f18\u7f3a\u70b9<\/h5>\n\n\n\n<h6 class=\"wp-block-heading\">\u4f18\u70b9<\/h6>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u9002\u7528\u4e8e\u8d8b\u52bf\u6027\u65f6\u95f4\u5e8f\u5217\uff1b<\/li>\n\n\n\n<li>\u6a21\u578b\u7ed3\u6784\u660e\u786e\u3001\u7406\u8bba\u6210\u719f\uff1b<\/li>\n\n\n\n<li>\u5bf9\u5c0f\u6837\u672c\u65f6\u95f4\u5e8f\u5217\u4e5f\u6709\u6548\uff1b<\/li>\n\n\n\n<li>\u5177\u6709\u53ef\u89e3\u91ca\u6027\uff08\u53c2\u6570\u542b\u4e49\u6e05\u6670\uff09\uff1b<\/li>\n\n\n\n<li>\u652f\u6301\u7f6e\u4fe1\u533a\u95f4\u9884\u6d4b\u3002<\/li>\n<\/ul>\n\n\n\n<h6 class=\"wp-block-heading\">\u7f3a\u70b9<\/h6>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u5bf9\u6570\u636e\u9884\u5904\u7406\u8981\u6c42\u9ad8\uff08\u9700\u5e73\u7a33\u6027\uff09\uff1b<\/li>\n\n\n\n<li>\u4e0d\u64c5\u957f\u6355\u6349<strong>\u975e\u7ebf\u6027\u6216\u590d\u6742\u6a21\u5f0f<\/strong>\uff1b<\/li>\n\n\n\n<li>\u5bf9\u5b63\u8282\u6027\u6570\u636e\u5904\u7406\u6709\u9650\uff08\u9700\u6269\u5c55\u4e3a SARIMA\uff09\uff1b<\/li>\n\n\n\n<li>\u957f\u671f\u9884\u6d4b\u6548\u679c\u53ef\u80fd\u4e0d\u5982\u6df1\u5ea6\u5b66\u4e60\u6a21\u578b\uff1b<\/li>\n\n\n\n<li>\u96be\u4ee5\u5904\u7406\u9ad8\u7ef4\u6216\u591a\u53d8\u91cf\u60c5\u5883\u3002<\/li>\n<\/ul>\n\n\n\n<h5 class=\"wp-block-heading\">\u516d\u3001ARIMA\u7684\u6269\u5c55\u6a21\u578b<\/h5>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>SARIMA\uff08\u5b63\u8282\u6027ARIMA\uff0cARIMA + \u5b63\u8282\u9879\uff09<\/strong>\uff1a\n<ul class=\"wp-block-list\">\n<li>\u8868\u793a\u4e3a SARIMA(p,d,q)(P,D,Q)[s]\uff1b<\/li>\n\n\n\n<li>\u9002\u5408\u5177\u6709\u5468\u671f\u6027\u7684\u65f6\u95f4\u5e8f\u5217\uff0c\u5982\u6c14\u6e29\u3001\u7535\u529b\u9700\u6c42\u7b49\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>ARIMAX\uff08\u5e26\u5916\u751f\u53d8\u91cf\uff09<\/strong>\uff1a\n<ul class=\"wp-block-list\">\n<li>\u589e\u52a0\u5916\u90e8\u53d8\u91cfX_t\uff0c\u6709\u52a9\u4e8e\u5efa\u6a21\u56e0\u679c\u5173\u7cfb\uff1b<\/li>\n\n\n\n<li>\u5e38\u7528\u4e8e\u7ecf\u6d4e\u9884\u6d4b\u3001\u653f\u7b56\u5efa\u6a21\u7b49\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>VAR\uff08\u5411\u91cf\u81ea\u56de\u5f52\uff09<\/strong>\uff1a\n<ul class=\"wp-block-list\">\n<li>\u591a\u53d8\u91cf\u65f6\u95f4\u5e8f\u5217\u6269\u5c55\u5f62\u5f0f\uff1b<\/li>\n\n\n\n<li>\u5efa\u6a21\u53d8\u91cf\u95f4\u76f8\u4e92\u5f71\u54cd\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>ARCH\/GARCH<\/strong>\uff1a\n<ul class=\"wp-block-list\">\n<li>\u9002\u7528\u4e8e\u91d1\u878d\u65f6\u95f4\u5e8f\u5217\uff0c\u5efa\u6a21\u65b9\u5dee\u7684\u65f6\u95f4\u53d8\u5316\u6027\uff08\u6ce2\u52a8\u6027\u5efa\u6a21\uff09\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<h5 class=\"wp-block-heading\">\u4e03\u3001\u5b9e\u9645\u5e94\u7528\u573a\u666f<\/h5>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u91d1\u878d\u5e02\u573a\u9884\u6d4b<\/strong>\uff1a\u5982\u80a1\u7968\u4ef7\u683c\u3001\u6c47\u7387\u3001\u5229\u7387\u65f6\u95f4\u5e8f\u5217\u5efa\u6a21\u3002<\/li>\n\n\n\n<li><strong>\u9500\u552e\u91cf\u9884\u6d4b<\/strong>\uff1a\u5546\u8d85\u65e5\u9500\u91cf\u3001\u7535\u5546\u6708\u9500\u91cf\u7b49\u3002<\/li>\n\n\n\n<li><strong>\u80fd\u6e90\u6d88\u8017\u9884\u6d4b<\/strong>\uff1a\u7535\u529b\u3001\u5929\u7136\u6c14\u3001\u6c34\u8d44\u6e90\u6d88\u8017\u5efa\u6a21\u3002<\/li>\n\n\n\n<li><strong>\u4ea4\u901a\u6d41\u91cf\u5206\u6790<\/strong>\uff1a\u5730\u94c1\u7ad9\u8fdb\u51fa\u4eba\u6570\u3001\u4ea4\u901a\u62e5\u5835\u60c5\u51b5\u3002<\/li>\n\n\n\n<li><strong>\u6c14\u8c61\u6570\u636e\u9884\u6d4b<\/strong>\uff1a\u6c14\u6e29\u3001\u964d\u96e8\u91cf\u3001\u98ce\u901f\u7b49\u65f6\u5e8f\u5efa\u6a21\u3002<\/li>\n\n\n\n<li><strong>\u5de5\u4e1a\u8bbe\u5907\u76d1\u63a7<\/strong>\uff1a\u5982\u4f20\u611f\u5668\u6570\u636e\u9884\u6d4b\u5f02\u5e38\u8d8b\u52bf\u7b49\u3002<\/li>\n<\/ol>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h5 class=\"wp-block-heading\">\u516b\u3001Python\u4ee3\u7801\u7b80\u8981\u793a\u4f8b<\/h5>\n\n\n\n<p class=\"wp-block-paragraph\">\u4f7f\u7528 <code>statsmodels<\/code>\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\"><code>import pandas as pd<br>import matplotlib.pyplot as plt<br>from statsmodels.tsa.arima.model import ARIMA<br><br># \u52a0\u8f7d\u65f6\u95f4\u5e8f\u5217\u6570\u636e<br>data = pd.read_csv('timeseries.csv', index_col='Date', parse_dates=True)<br><br># \u62df\u5408 ARIMA(1,1,1) \u6a21\u578b<br>model = ARIMA(data, order=(1, 1, 1))<br>result = model.fit()<br><br># \u6a21\u578b\u6458\u8981<br>print(result.summary())<br><br># \u9884\u6d4b\u672a\u676510\u6b65<br>forecast = result.get_forecast(steps=10)<br>forecast_mean = forecast.predicted_mean<br>forecast_ci = forecast.conf_int()<br><br># \u53ef\u89c6\u5316\u9884\u6d4b\u7ed3\u679c<br>plt.plot(data, label='Observed')<br>plt.plot(forecast_mean, label='Forecast')<br>plt.fill_between(forecast_ci.index, forecast_ci.iloc[:, 0], forecast_ci.iloc[:, 1], color='pink', alpha=0.3)<br>plt.legend()<br>plt.show()<br><\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading has-text-align-center\"><strong> ARIMA \u6a21\u578b\u4e0e\u5176\u6269\u5c55\uff08SARIMA\u3001ARIMAX\uff09\u4ee5\u53ca\u4e0e\u6df1\u5ea6\u5b66\u4e60\u6a21\u578b\uff08\u5982 LSTM\uff09\u7684\u6bd4\u8f83\u5206\u6790<\/strong><\/h4>\n\n\n\n<h5 class=\"wp-block-heading\">\u4e00\u3001ARIMA \u53ca\u6269\u5c55\u6a21\u578b\u5bf9\u6bd4\uff1aSARIMA \u4e0e ARIMAX<\/h5>\n\n\n\n<h6 class=\"wp-block-heading\">1.1 ARIMA \u56de\u987e<\/h6>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u9002\u7528\u4e8e<strong>\u5355\u53d8\u91cf\u3001\u975e\u5b63\u8282\u6027\u3001\u7ebf\u6027\u8d8b\u52bf<\/strong>\u65f6\u95f4\u5e8f\u5217\u3002<\/li>\n\n\n\n<li>\u5efa\u6a21\u5bf9\u8c61\uff1a\u5e73\u7a33\u5e8f\u5217\u6216\u7ecf\u5dee\u5206\u540e\u7684\u975e\u5e73\u7a33\u5e8f\u5217\u3002<\/li>\n<\/ul>\n\n\n\n<h6 class=\"wp-block-heading\">1.2 SARIMA\uff08\u5b63\u8282\u6027 ARIMA\uff09<\/h6>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u5b9a\u4e49<\/strong>\uff1aSARIMA \u6a21\u578b\u5f15\u5165\u4e86\u5b63\u8282\u6027\u9879\uff0c\u7528\u4e8e\u5efa\u6a21\u5468\u671f\u6027\u7279\u5f81\uff0c\u5982\u6708\u5ea6\u3001\u5b63\u5ea6\u3001\u5e74\u5ea6\u6ce2\u52a8\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u8868\u793a<\/strong>\uff1aSARIMA(p,d,q)(P,D,Q)<sub>s<\/sub><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5176\u4e2d\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>p,d,q\uff1a\u975e\u5b63\u8282\u9879\uff08\u4e0e ARIMA \u76f8\u540c\uff09\uff1b<\/li>\n\n\n\n<li>P,D,Q\uff1a\u5b63\u8282\u9879\u7684\u81ea\u56de\u5f52\u3001\u5dee\u5206\u3001\u6ed1\u52a8\u5e73\u5747\uff1b<\/li>\n\n\n\n<li>s\uff1a\u5b63\u8282\u5468\u671f\uff08\u5982 s=12 \u8868\u793a\u4e00\u5e7412\u4e2a\u6708\uff09\uff1b<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u793a\u4f8b<\/strong>\uff1a\u7535\u529b\u4f7f\u7528\u91cf\u5728\u6bcf\u5e74\u51ac\u5929\u5cf0\u503c\u9ad8\uff0c\u590f\u5929\u6b21\u9ad8\uff0cSARIMA \u53ef\u5efa\u6a21\u8fd9\u79cd\u5b63\u8282\u884c\u4e3a\u3002<\/p>\n\n\n\n<h6 class=\"wp-block-heading\">1.3 ARIMAX\uff08\u5e26\u5916\u751f\u53d8\u91cf\uff09<\/h6>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u5b9a\u4e49<\/strong>\uff1a\u5f15\u5165\u5916\u751f\u53d8\u91cf X<sub>t<\/sub>\u200b\uff0c\u7528\u4e8e\u5efa\u6a21\u56e0\u679c\u9a71\u52a8\u56e0\u7d20\u7684\u5f71\u54cd\u3002y<sub>t<\/sub>=ARIMA(p,d,q)+\u03b2X<sub>t<\/sub>+\u03f5<sub>t<\/sub><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u9002\u5408\u573a\u666f<\/strong>\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u5de5\u4e1a\u8bbe\u5907\u6545\u969c\u7387\u9884\u6d4b\u65f6\uff0c\u52a0\u5165\u73af\u5883\u6e29\u5ea6\u3001\u6e7f\u5ea6\u3001\u8f7d\u8377\u7b49\u4f20\u611f\u5668\u53d8\u91cf\uff1b<\/li>\n\n\n\n<li>\u9500\u552e\u9884\u6d4b\u65f6\uff0c\u52a0\u5165\u4fc3\u9500\u6d3b\u52a8\u3001\u8282\u5047\u65e5\u7b49\u5e72\u9884\u56e0\u5b50\uff1b<\/li>\n\n\n\n<li>\u7535\u68af\u4f7f\u7528\u6b21\u6570\u9884\u6d4b\u65f6\uff0c\u8003\u8651\u5929\u6c14\u3001\u5de5\u4f5c\u65e5\/\u8282\u5047\u65e5\u3001\u697c\u5c42\u4eba\u6570\u7b49\u56e0\u7d20\u3002<\/li>\n<\/ul>\n\n\n\n<h5 class=\"wp-block-heading\">\u4e8c\u3001\u4e0e\u6df1\u5ea6\u5b66\u4e60\u6a21\u578b\uff08LSTM\uff09\u5bf9\u6bd4\u5206\u6790<\/h5>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>\u7279\u5f81\u7ef4\u5ea6<\/th><th>ARIMA\/SARIMA<\/th><th>ARIMAX<\/th><th>LSTM\uff08Long Short-Term Memory\uff09<\/th><\/tr><\/thead><tbody><tr><td>\u7c7b\u578b<\/td><td>\u7ebf\u6027\u6a21\u578b<\/td><td>\u7ebf\u6027+\u5916\u56e0<\/td><td>\u975e\u7ebf\u6027\u795e\u7ecf\u7f51\u7edc<\/td><\/tr><tr><td>\u5904\u7406\u7279\u6027<\/td><td>\u5355\u53d8\u91cf\uff1b\u9700\u5e73\u7a33<\/td><td>\u591a\u53d8\u91cf\uff1b\u53ef\u5efa\u6a21\u56e0\u679c<\/td><td>\u591a\u53d8\u91cf\uff1b\u9002\u7528\u4e8e\u590d\u6742\u6a21\u5f0f<\/td><\/tr><tr><td>\u6a21\u578b\u89e3\u91ca\u6027<\/td><td>\u9ad8\uff08\u7cfb\u6570\u53ef\u89e3\u91ca\uff09<\/td><td>\u9ad8\uff08\u53ef\u91cf\u5316\u5916\u56e0\u4f5c\u7528\uff09<\/td><td>\u4f4e\uff08\u4e3a\u201c\u9ed1\u76d2\u201d\uff09<\/td><\/tr><tr><td>\u957f\u671f\u9884\u6d4b\u80fd\u529b<\/td><td>\u5f31\uff08\u7ebf\u6027\uff09<\/td><td>\u4e00\u822c<\/td><td>\u5f3a\uff08\u53ef\u5efa\u6a21\u957f\u671f\u4f9d\u8d56\uff09<\/td><\/tr><tr><td>\u5bf9\u5b63\u8282\u6027\u652f\u6301<\/td><td>SARIMA<\/td><td>\u9650\u652f\u6301<\/td><td>LSTM \u901a\u8fc7\u5e8f\u5217\u8bad\u7ec3\u81ea\u52a8\u6355\u6349<\/td><\/tr><tr><td>\u8bad\u7ec3\u6570\u636e\u9700\u6c42<\/td><td>\u5c11\u91cf\u6837\u672c\u5373\u53ef<\/td><td>\u4e2d\u7b49<\/td><td>\u9700\u5927\u91cf\u6570\u636e<\/td><\/tr><tr><td>\u8bad\u7ec3\u901f\u5ea6<\/td><td>\u5feb\uff08\u57fa\u4e8eMLE\uff09<\/td><td>\u5feb<\/td><td>\u6162\uff08\u9700GPU\/\u8fed\u4ee3\uff09<\/td><\/tr><tr><td>\u5e38\u89c1\u573a\u666f<\/td><td>\u8d22\u52a1\u3001\u7ecf\u6d4e\u3001\u8fc7\u7a0b\u63a7\u5236<\/td><td>\u5de5\u4e1a\u9884\u6d4b\u3001\u5e72\u9884\u5206\u6790<\/td><td>\u7535\u68af\u6545\u969c\u9884\u6d4b\u3001\u56fe\u50cf\/\u8bed\u97f3\/\u4fe1\u53f7\u9884\u6d4b\u7b49\u590d\u6742\u573a\u666f<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u603b\u7ed3<\/strong>\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u82e5\u6570\u636e\u7ebf\u6027\/\u5f31\u6ce2\u52a8\u3001\u6837\u672c\u91cf\u6709\u9650\u3001\u6a21\u578b\u89e3\u91ca\u6027\u8981\u6c42\u9ad8 \u2192 \u7528 ARIMA\/ARIMAX\uff1b<\/li>\n\n\n\n<li>\u82e5\u5b58\u5728\u5468\u671f\u6027 \u2192 SARIMA\uff1b<\/li>\n\n\n\n<li>\u82e5\u6570\u636e\u591a\u53d8\u91cf\u3001\u975e\u7ebf\u6027\u3001\u6ce2\u52a8\u5f3a\u3001\u6570\u636e\u91cf\u5927 \u2192 LSTM \u66f4\u4f18\u3002<\/li>\n<\/ul>\n\n\n\n<h5 class=\"wp-block-heading\">\u4e09\u3001\u5728\u5de5\u4e1a\u4f20\u611f\u5668\u4e0e\u7535\u68af\u7cfb\u7edf\u4e2d\u7684\u5e94\u7528\u6bd4\u8f83<\/h5>\n\n\n\n<h6 class=\"wp-block-heading\">3.1 \u5de5\u4e1a\u4f20\u611f\u5668\uff08\u5982\u632f\u52a8\u3001\u7535\u6d41\u3001\u6e29\u5ea6\uff09<\/h6>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>\u6a21\u578b<\/th><th>\u5e94\u7528<\/th><th>\u8868\u73b0<\/th><\/tr><\/thead><tbody><tr><td>ARIMA<\/td><td>\u5bf9\u5355\u4e00\u4f20\u611f\u5668\u6570\u636e\u8fdb\u884c\u77ed\u671f\u9884\u6d4b\uff0c\u5982\u7535\u673a\u7535\u6d41\u53d8\u5316\u8d8b\u52bf<\/td><td>\u51c6\u786e\u5ea6\u9ad8\uff0c\u90e8\u7f72\u7b80\u5355<\/td><\/tr><tr><td>SARIMA<\/td><td>\u5bf9\u632f\u52a8\u6570\u636e\u4e2d\u5b58\u5728\u5468\u671f\u6027\u53d8\u5316\u7684\u573a\u5408\uff08\u5982\u6bcf\u65e5\u8fd0\u8f6c\u5468\u671f\uff09<\/td><td>\u4f18\u4e8e ARIMA<\/td><\/tr><tr><td>ARIMAX<\/td><td>\u5f15\u5165\u6e29\u5ea6\/\u8d1f\u8f7d\/\u8f6c\u901f\u7b49\u4f20\u611f\u5668\u6570\u636e\u5efa\u6a21\u7535\u6d41\u8d8b\u52bf<\/td><td>\u53ef\u7528\u4e8e\u6545\u969c\u524d\u5146\u5efa\u6a21<\/td><\/tr><tr><td>LSTM<\/td><td>\u591a\u4f20\u611f\u5668\u8054\u5408\u5efa\u6a21\uff1b\u9002\u5408\u5f02\u5e38\u68c0\u6d4b\u3001\u7a81\u53d8\u8bc6\u522b<\/td><td>\u51c6\u786e\u5ea6\u9ad8\u4f46\u9700\u5927\u6570\u636e\u8bad\u7ec3<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h6 class=\"wp-block-heading\">3.2 \u7535\u68af\u6545\u969c\u9884\u6d4b\uff08\u57fa\u4e8e\u52a0\u901f\u5ea6\u3001\u7535\u6d41\u3001\u95e8\u4f53\u72b6\u6001\u7b49\uff09<\/h6>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>ARIMA<\/strong>\uff1a\u9884\u6d4b\u67d0\u4e2a\u901a\u9053\uff08\u5982\u95e8\u7535\u673a\u7535\u6d41\uff09\u7684\u672a\u6765\u8d8b\u52bf\u503c\uff0c\u5224\u65ad\u662f\u5426\u5f02\u5e38\uff1b<\/li>\n\n\n\n<li><strong>ARIMAX<\/strong>\uff1a\u8003\u8651\u632f\u52a8+\u6e29\u6e7f\u5ea6\u5f71\u54cd\u95e8\u6545\u969c\uff0c\u9002\u5408\u5efa\u6a21<strong>\u7269\u7406\u56e0\u679c\u673a\u5236<\/strong>\uff1b<\/li>\n\n\n\n<li><strong>LSTM<\/strong>\uff1a\u5c06\u591a\u4e2a\u5e8f\u5217\uff08\u95e8\u7535\u6d41\u3001\u95e8\u901f\u5ea6\u3001\u7535\u538b\u6ce2\u5f62\u7b49\uff09\u7edf\u4e00\u8f93\u5165\uff0c\u9002\u5408<strong>\u6355\u6349\u590d\u6742\u7684\u6545\u969c\u6a21\u5f0f<\/strong>\u3002<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u4f8b\u5982\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u82e5\u51fa\u73b0\u95e8\u673a\u7535\u6d41\u7a81\u53d8 \u2192 ARIMA \u80fd\u77ed\u671f\u8bc6\u522b\uff1b<\/li>\n\n\n\n<li>\u82e5\u5728\u9ad8\u6e7f\u5ea6+\u9891\u7e41\u5f00\u542f\u60c5\u51b5\u4e0b\u6545\u969c\u6982\u7387\u4e0a\u5347 \u2192 ARIMAX \u53ef\u91cf\u5316\u8be5\u98ce\u9669\uff1b<\/li>\n\n\n\n<li>\u82e5\u4ece\u591a\u4e2a\u5e8f\u5217\u4e2d\u63d0\u53d6\u201c\u95e8\u5361\u987f\u524d\u5146\u6a21\u5f0f\u201d \u2192 LSTM \u6700\u5408\u9002\u3002<\/li>\n<\/ul>\n\n\n\n<h5 class=\"wp-block-heading\">\u56db\u3001\u96c6\u6210\u5efa\u6a21\u5efa\u8bae\uff1a\u7edf\u8ba1+\u6df1\u5ea6\u5b66\u4e60\u878d\u5408<\/h5>\n\n\n\n<p class=\"wp-block-paragraph\">\u5728\u5de5\u7a0b\u5b9e\u8df5\u4e2d\uff0c\u5f88\u591a\u56e2\u961f\u91c7\u53d6**\u201c\u7edf\u8ba1\u5efa\u6a21 + \u6df1\u5ea6\u6a21\u578b\u201d\u7684\u96c6\u6210\u7b56\u7565**\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u5148\u7528 ARIMA \u5efa\u6a21\u5e76\u5254\u9664\u7ebf\u6027\u90e8\u5206\u6b8b\u5dee<\/strong>\uff1b<\/li>\n\n\n\n<li><strong>\u518d\u5c06\u6b8b\u5dee\u90e8\u5206\u7528 LSTM\/GRU \u5efa\u6a21<\/strong>\uff0c\u5b66\u4e60\u975e\u7ebf\u6027\u6ce2\u52a8\uff1b<\/li>\n\n\n\n<li><strong>\u6700\u7ec8\u9884\u6d4b = ARIMA\u9884\u6d4b + LSTM\u6b8b\u5dee\u4fee\u6b63\u9884\u6d4b<\/strong>\u3002<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u79cd\u65b9\u5f0f\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u4fdd\u7559\u4e86\u89e3\u91ca\u6027\uff1b<\/li>\n\n\n\n<li>\u53c8\u83b7\u5f97\u4e86\u590d\u6742\u975e\u7ebf\u6027\u80fd\u529b\uff1b<\/li>\n\n\n\n<li>\u5728\u5de5\u4e1a\u7cfb\u7edf\u4e2d\u53ef\u589e\u5f3a\u6a21\u578b<strong>\u7a33\u5b9a\u6027\u3001\u9c81\u68d2\u6027\u548c\u51c6\u786e\u7387<\/strong>\u3002<\/li>\n<\/ul>\n\n\n\n<h5 class=\"wp-block-heading\">\u4e94\u3001Python \u7b80\u5316\u5bf9\u6bd4\u793a\u4f8b<\/h5>\n\n\n\n<h6 class=\"wp-block-heading\">ARIMAX \u793a\u4f8b\uff1a<\/h6>\n\n\n\n<pre class=\"wp-block-preformatted\"><code>from statsmodels.tsa.statespace.sarimax import SARIMAX<br><br># y: \u95e8\u673a\u7535\u6d41\u65f6\u95f4\u5e8f\u5217\uff0cexog: \u5916\u90e8\u53d8\u91cf\u5982\u6e29\u5ea6\u3001\u6e7f\u5ea6\u7b49<br>model = SARIMAX(y, exog=exog, order=(1,1,1))<br>results = model.fit()<br>forecast = results.get_forecast(steps=10, exog=exog_future)<br><\/code><\/pre>\n\n\n\n<h6 class=\"wp-block-heading\">LSTM \u793a\u4f8b\uff08\u591a\u4f20\u611f\u5668\uff09\uff1a<\/h6>\n\n\n\n<pre class=\"wp-block-preformatted\">python\u590d\u5236\u7f16\u8f91<code>from keras.models import Sequential\nfrom keras.layers import LSTM, Dense\n\nmodel = Sequential()\nmodel.add(LSTM(64, input_shape=(timesteps, features)))\nmodel.add(Dense(1))  # \u9884\u6d4b\u95e8\u7535\u6d41\u4e0b\u4e00\u6b65\u503c\nmodel.compile(loss='mse', optimizer='adam')\nmodel.fit(X_train, y_train, epochs=20, batch_size=32)\n<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading has-text-align-center\"><strong>\u5b8c\u6574\u7684ARIMA vs ARIMAX vs LSTM \u6545\u969c\u9884\u6d4b\u5b9e\u9a8c\u6846\u67b6\u8bbe\u8ba1<\/strong><\/h4>\n\n\n\n<h5 class=\"wp-block-heading\">\u4e00\u3001\u5e94\u7528\u80cc\u666f\u4e0e\u6570\u636e\u8bbe\u5b9a<\/h5>\n\n\n\n<p class=\"wp-block-paragraph\">\u5047\u8bbe\u6211\u4eec\u9488\u5bf9\u67d0\u54c1\u724c\u7535\u68af\u95e8\u7cfb\u7edf\u8fdb\u884c\u9884\u6d4b\u6027\u7ef4\u62a4\uff0c\u5df2\u5b89\u88c5\u4ee5\u4e0b\u4f20\u611f\u5668\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>\u4f20\u611f\u5668\u7c7b\u578b<\/th><th>\u91c7\u96c6\u5185\u5bb9<\/th><th>\u5355\u4f4d<\/th><th>\u91c7\u6837\u9891\u7387<\/th><\/tr><\/thead><tbody><tr><td>\u7535\u673a\u7535\u6d41\u4f20\u611f\u5668<\/td><td>\u95e8\u4f53\u5f00\u5408\u65f6\u7684\u7535\u6d41 RMS<\/td><td>A<\/td><td>10 Hz\uff08\u6216\u6309\u5468\u671f\u5747\u503c\uff09<\/td><\/tr><tr><td>\u52a0\u901f\u5ea6\u4f20\u611f\u5668<\/td><td>\u95e8\u4f53\u632f\u52a8 RMS<\/td><td>m\/s\u00b2<\/td><td>100 Hz \u2192 \u63d0\u53d6\u7279\u5f81<\/td><\/tr><tr><td>\u6e29\u6e7f\u5ea6\u4f20\u611f\u5668<\/td><td>\u5468\u56f4\u73af\u5883\u6e29\u5ea6\u4e0e\u6e7f\u5ea6<\/td><td>\u2103 \/ %RH<\/td><td>1 Hz<\/td><\/tr><tr><td>\u72b6\u6001\u6807\u7b7e<\/td><td>\u662f\u5426\u53d1\u751f\u95e8\u5361\u3001\u5361\u987f\u7b49\u6545\u969c<\/td><td>0 \u6216 1<\/td><td>\u7531\u4eba\u5de5\u6807\u6ce8\u6216\u5f02\u5e38\u68c0\u6d4b\u751f\u6210<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u6211\u4eec\u4ee5<strong>\u7535\u6d41 RMS \u5e8f\u5217\u4e3a\u4e3b\u9884\u6d4b\u5bf9\u8c61<\/strong>\uff0c\u5e0c\u671b\u80fd\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u5bf9\u7535\u6d41\u672a\u6765\u77ed\u65f6\u95f4\u5185\u53d8\u5316\u8d8b\u52bf\u505a\u9884\u6d4b\uff1b<\/li>\n\n\n\n<li>\u6355\u6349\u6f5c\u5728\u6545\u969c\u524d\u5146\uff1b<\/li>\n\n\n\n<li>\u6bd4\u8f83 ARIMA\u3001ARIMAX\u3001LSTM \u6a21\u578b\u7684\u4f18\u52a3\u3002<\/li>\n<\/ol>\n\n\n\n<h5 class=\"wp-block-heading\">\u4e8c\u3001\u5efa\u6a21\u76ee\u6807\u4e0e\u9884\u6d4b\u53d8\u91cf<\/h5>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u9884\u6d4b\u76ee\u6807<\/strong>\uff08y\uff09\uff1a\u95e8\u4f53\u7535\u673a\u7535\u6d41 RMS\uff08\u4e0b\u4e00\u65f6\u523b\u6216\u672a\u6765 N \u6b65\u7684\u503c\uff09<\/li>\n\n\n\n<li><strong>\u5916\u751f\u53d8\u91cf\uff08ARIMAX\uff09\/\u7279\u5f81\u53d8\u91cf\uff08LSTM\uff09<\/strong>\uff1a\n<ul class=\"wp-block-list\">\n<li>\u632f\u52a8 RMS\uff08\u4ee3\u8868\u673a\u68b0\u7cfb\u7edf\u5f02\u5e38\uff09<\/li>\n\n\n\n<li>\u6e29\u5ea6\uff08\u5f71\u54cd\u95e8\u4f53\u963b\u529b\u4e0e\u7535\u673a\u6027\u80fd\uff09<\/li>\n\n\n\n<li>\u6e7f\u5ea6\uff08\u5f71\u54cd\u63a5\u89e6\u5668\u3001\u8f68\u9053\uff09<\/li>\n\n\n\n<li>\u95e8\u4f53\u8fd0\u52a8\u65b9\u5411\uff08\u5f00\/\u5173\uff09<\/li>\n\n\n\n<li>\u7535\u538b\u7535\u5e73\uff08\u5982\u6709\u91c7\u96c6\uff09<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<h5 class=\"wp-block-heading\">\u4e09\u3001\u4e09\u79cd\u6a21\u578b\u5efa\u6a21\u6d41\u7a0b\u8bbe\u8ba1<\/h5>\n\n\n\n<h6 class=\"wp-block-heading\">3.1 ARIMA \u6a21\u578b\u6d41\u7a0b\uff08\u5355\u53d8\u91cf\uff09<\/h6>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u5bf9\u7535\u6d41 RMS \u6570\u636e\u505a\u5dee\u5206\u5904\u7406\uff0c\u4f7f\u4e4b\u5e73\u7a33\uff1b<\/li>\n\n\n\n<li>\u7528 ACF \/ PACF \u5224\u65ad\u5408\u9002\u7684 (p,d,q) \u503c\uff1b<\/li>\n\n\n\n<li>\u4f7f\u7528 <code>statsmodels.tsa.arima.model.ARIMA<\/code> \u8fdb\u884c\u62df\u5408\uff1b<\/li>\n\n\n\n<li>\u9884\u6d4b\u672a\u6765 N \u6b65\u7535\u6d41\u503c\uff1b<\/li>\n\n\n\n<li>\u6b8b\u5dee\u68c0\u9a8c\uff08\u767d\u566a\u58f0\u3001\u6b63\u6001\u6027\uff09\uff1b<\/li>\n\n\n\n<li>\u8bb0\u5f55 RMSE \/ MAE \u7b49\u6307\u6807\u3002<\/li>\n<\/ol>\n\n\n\n<h6 class=\"wp-block-heading\">3.2 ARIMAX \u6a21\u578b\u6d41\u7a0b\uff08\u591a\u53d8\u91cf+\u56e0\u679c\u5efa\u6a21\uff09<\/h6>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u5c06\u7535\u6d41 RMS \u4f5c\u4e3a\u76ee\u6807\uff0c\u632f\u52a8\/\u6e29\u6e7f\u5ea6\u7b49\u4f5c\u4e3a exog\uff1b<\/li>\n\n\n\n<li>\u5bf9\u5404\u53d8\u91cf\u505a\u540c\u6b65\u4e0e\u7f3a\u5931\u503c\u63d2\u8865\uff1b<\/li>\n\n\n\n<li>\u7528 <code>SARIMAX<\/code> \u62df\u5408\u6a21\u578b\uff1a python\u590d\u5236\u7f16\u8f91<code>SARIMAX(endog=y_train, exog=X_train, order=(p,d,q))<\/code><\/li>\n\n\n\n<li>\u4f7f\u7528\u672a\u6765\u5916\u751f\u53d8\u91cf <code>X_future<\/code> \u9884\u6d4b <code>y_future<\/code>\uff1b<\/li>\n\n\n\n<li>\u5206\u6790\u5404\u5916\u751f\u53d8\u91cf\u7684\u7cfb\u6570\u663e\u8457\u6027\uff1b<\/li>\n\n\n\n<li>\u68c0\u67e5\u6b8b\u5dee\u3001\u8bc4\u4f30\u6027\u80fd\u3002<\/li>\n<\/ol>\n\n\n\n<h6 class=\"wp-block-heading\">3.3 LSTM \u6a21\u578b\u6d41\u7a0b\uff08\u6df1\u5ea6\u5b66\u4e60\u591a\u53d8\u91cf\uff09<\/h6>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u5bf9\u6240\u6709\u65f6\u95f4\u5e8f\u5217\u5f52\u4e00\u5316\uff08\u5982 MinMaxScaler\uff09\uff1b<\/li>\n\n\n\n<li>\u4ee5\u6ed1\u7a97\u65b9\u5f0f\u751f\u6210\u8bad\u7ec3\u96c6\uff1a\n<ul class=\"wp-block-list\">\n<li>\u8f93\u5165\uff1a\u591a\u53d8\u91cf\u8fc7\u53bb T \u6b65\u7684\u65f6\u95f4\u7a97\u5e8f\u5217\uff1b<\/li>\n\n\n\n<li>\u8f93\u51fa\uff1a\u7535\u6d41 RMS \u4e0b\u4e00\u6b65\u6216\u672a\u6765 N \u6b65\uff1b<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u7f51\u7edc\u7ed3\u6784\uff1a\n<ul class=\"wp-block-list\">\n<li>\u8f93\u5165\u5c42\uff1a[T \u6b65 \u00d7 n \u7279\u5f81]<\/li>\n\n\n\n<li>LSTM\uff08\u6216 Bi-LSTM\uff09+ Dropout<\/li>\n\n\n\n<li>Dense \u8f93\u51fa\u5c42<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u635f\u5931\u51fd\u6570\uff1aMSE<\/li>\n\n\n\n<li>\u8bad\u7ec3\u9a8c\u8bc1\u96c6\u5212\u5206\u3001Early Stopping<\/li>\n\n\n\n<li>\u9884\u6d4b\u540e\u9006\u5f52\u4e00\u5316\uff0c\u8bb0\u5f55\u8bef\u5dee<\/li>\n<\/ol>\n\n\n\n<h5 class=\"wp-block-heading\">\u56db\u3001\u9884\u6d4b\u6027\u80fd\u8bc4\u4f30\u6307\u6807<\/h5>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>\u6307\u6807<\/th><th>\u542b\u4e49<\/th><th>\u8bf4\u660e<\/th><\/tr><\/thead><tbody><tr><td><strong>RMSE<\/strong><\/td><td>\u5747\u65b9\u6839\u8bef\u5dee<\/td><td>\u5bf9\u5927\u504f\u5dee\u60e9\u7f5a\u66f4\u91cd<\/td><\/tr><tr><td><strong>MAE<\/strong><\/td><td>\u5e73\u5747\u7edd\u5bf9\u8bef\u5dee<\/td><td>\u5bf9\u6240\u6709\u8bef\u5dee\u5e73\u7b49\u5bf9\u5f85<\/td><\/tr><tr><td><strong>MAPE<\/strong><\/td><td>\u5e73\u5747\u767e\u5206\u6bd4\u8bef\u5dee<\/td><td>\u9700\u76ee\u6807\u503c\u4e0d\u4e3a\u96f6<\/td><\/tr><tr><td><strong>R\u00b2 Score<\/strong><\/td><td>\u62df\u5408\u4f18\u5ea6<\/td><td>\u8d8a\u63a5\u8fd11\u8d8a\u597d<\/td><\/tr><tr><td><strong>\u6b8b\u5dee\u5206\u5e03\u6b63\u6001\u6027<\/strong><\/td><td>\u6b63\u6001\u6027\u68c0\u9a8c<\/td><td>\u62df\u5408\u7a33\u5b9a\u6027\u53c2\u8003<\/td><\/tr><tr><td><strong>\u9884\u6d4b\u65f6\u5ef6<\/strong><\/td><td>\u6a21\u578b\u63a8\u7406\u901f\u5ea6<\/td><td>\u5b9e\u65f6\u573a\u666f\u91cd\u8981<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h5 class=\"wp-block-heading\">\u4e94\u3001\u5b9e\u9a8c\u8bbe\u8ba1\u4e0e\u5bf9\u6bd4\u5efa\u8bae<\/h5>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>\u7ef4\u5ea6<\/th><th>ARIMA<\/th><th>ARIMAX<\/th><th>LSTM<\/th><\/tr><\/thead><tbody><tr><td>\u6570\u636e\u9700\u6c42<\/td><td>\u5c11\u91cf<\/td><td>\u4e2d\u7b49<\/td><td>\u8f83\u591a<\/td><\/tr><tr><td>\u6570\u636e\u51c6\u5907<\/td><td>\u4ec5\u9700\u76ee\u6807\u5e8f\u5217<\/td><td>\u9700\u6536\u96c6\u540c\u6b65\u5916\u90e8\u53d8\u91cf<\/td><td>\u591a\u53d8\u91cf\u540c\u6b65\u7a97\u53e3\u5904\u7406<\/td><\/tr><tr><td>\u89e3\u91ca\u6027<\/td><td>\u5f3a<\/td><td>\u5f3a\uff08\u56e0\u679c\u4f5c\u7528\uff09<\/td><td>\u5f31\uff08\u9ed1\u76d2\uff09<\/td><\/tr><tr><td>\u5f02\u5e38\u524d\u5146\u8bc6\u522b<\/td><td>\u4e00\u822c\uff08\u4f9d\u8d56\u6ce2\u52a8\uff09<\/td><td>\u597d\uff08\u5f15\u5165\u56e0\u679c\uff09<\/td><td>\u6700\u597d\uff08\u53ef\u8bc6\u522b\u590d\u6742\u975e\u7ebf\u6027\u524d\u5146\uff09<\/td><\/tr><tr><td>\u8bad\u7ec3\u65f6\u95f4<\/td><td>\u5feb<\/td><td>\u5feb<\/td><td>\u8f83\u957f\uff08\u9700GPU\uff09<\/td><\/tr><tr><td>\u9002\u5408\u573a\u666f<\/td><td>\u7b80\u5355\u8d8b\u52bf\u9884\u6d4b<\/td><td>\u591a\u56e0\u7d20\u6ce2\u52a8\u5efa\u6a21<\/td><td>\u9ad8\u590d\u6742\u6545\u969c\u9884\u6d4b\u3001\u7279\u5f81\u8054\u52a8\u6316\u6398<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u5efa\u8bae\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u82e5\u7cfb\u7edf\u6570\u636e\u4e0d\u7a33\u5b9a\u3001\u590d\u6742\u5173\u8054\u591a\uff0c\u9009\u7528 LSTM\uff1b<\/li>\n\n\n\n<li>\u82e5\u5e0c\u671b\u6a21\u578b\u53ef\u90e8\u7f72\u5728\u4f4e\u7b97\u529b\u7ec8\u7aef\uff0c\u63a8\u8350 ARIMAX\uff1b<\/li>\n\n\n\n<li>\u82e5\u6570\u636e\u6837\u672c\u5c11\u3001\u5148\u9a8c\u8bc1\u8d8b\u52bf\u53ef\u7528\u6027 \u2192 \u5148\u8bd5 ARIMA \u4f5c\u4e3a baseline\u3002<\/li>\n<\/ul>\n\n\n\n<h5 class=\"wp-block-heading\">\u516d\u3001\u53ef\u89c6\u5316\u4e0e\u7ed3\u679c\u89e3\u91ca\u5efa\u8bae<\/h5>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u9884\u6d4b vs \u5b9e\u9645\u66f2\u7ebf<\/strong>\uff1a\n<ul class=\"wp-block-list\">\n<li>\u6298\u7ebf\u56fe\u5bf9\u6bd43\u79cd\u6a21\u578b\u9884\u6d4b\u7ed3\u679c\u4e0e\u5b9e\u9645\u6570\u636e\uff1b<\/li>\n\n\n\n<li>\u53ef\u6807\u8bb0\u201c\u6545\u969c\u524d10\u5206\u949f\u201d\u5904\uff0c\u770b\u54ea\u4e2a\u6a21\u578b\u63d0\u524d\u8bc6\u522b\u51fa\u8d8b\u52bf\u5f02\u5e38\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>\u6b8b\u5dee\u5206\u5e03\u56fe<\/strong>\uff1a\n<ul class=\"wp-block-list\">\n<li>\u68c0\u67e5\u662f\u5426\u5747\u503c\u4e3a0\u3001\u5206\u5e03\u662f\u5426\u8fd1\u4f3c\u6b63\u6001\uff1b<\/li>\n\n\n\n<li>\u53ef\u7528 Q-Q \u56fe\u3001Shapiro-Wilk \u6d4b\u8bd5\u8f85\u52a9\u5224\u65ad\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>\u7279\u5f81\u91cd\u8981\u6027\u5206\u6790<\/strong>\uff08ARIMAX\uff09\uff1a\n<ul class=\"wp-block-list\">\n<li>\u67e5\u770b\u6a21\u578b\u7cfb\u6570\u663e\u8457\u6027\uff08t\u503c\/P\u503c\uff09\uff1b<\/li>\n\n\n\n<li>\u5206\u6790\u6e29\u5ea6\/\u6e7f\u5ea6\u7b49\u5916\u90e8\u56e0\u7d20\u5bf9\u7535\u6d41\u6ce2\u52a8\u5f71\u54cd\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>\u9884\u6d4b\u8bef\u5dee\u6761\u5f62\u56fe\uff08RMSE, MAE, MAPE\uff09<\/strong>\uff1a\n<ul class=\"wp-block-list\">\n<li>\u660e\u786e\u91cf\u5316\u4e09\u79cd\u6a21\u578b\u6027\u80fd\u4f18\u52a3\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>ARIMA\uff08AutoRegressive Integrated Moving Average\uff0c\u81ea\u56de\u5f52\u6ed1\u52a8\u5e73\u5747\u6574 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"set","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[8],"tags":[39,40],"class_list":["post-6053","post","type-post","status-publish","format-standard","hentry","category-tech","tag-ai","tag-iot"],"rttpg_featured_image_url":null,"rttpg_author":{"display_name":"NullThought","author_link":"https:\/\/nullthought.net\/?author=1"},"rttpg_comment":0,"rttpg_category":"<a href=\"https:\/\/nullthought.net\/?cat=8\" rel=\"category\">Tech<\/a>","rttpg_excerpt":"ARIMA\uff08AutoRegressive Integrated Moving Average\uff0c\u81ea\u56de\u5f52\u6ed1\u52a8\u5e73\u5747\u6574&hellip;","_links":{"self":[{"href":"https:\/\/nullthought.net\/index.php?rest_route=\/wp\/v2\/posts\/6053","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/nullthought.net\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/nullthought.net\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/nullthought.net\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/nullthought.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=6053"}],"version-history":[{"count":1,"href":"https:\/\/nullthought.net\/index.php?rest_route=\/wp\/v2\/posts\/6053\/revisions"}],"predecessor-version":[{"id":6056,"href":"https:\/\/nullthought.net\/index.php?rest_route=\/wp\/v2\/posts\/6053\/revisions\/6056"}],"wp:attachment":[{"href":"https:\/\/nullthought.net\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=6053"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/nullthought.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=6053"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/nullthought.net\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=6053"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}